Name
Title | ||
|---|---|---|
Augmented Precision Square Roots and 2-D Norms, and Discussion on Correctly Rounding sqrt(x^2+y^2) |
Abstract | ||
|---|---|---|
Define an "augmented precision" algorithm as an algorithm that returns, in precision-p floating-point arithmetic, its result as the unevaluated sum of two floating-point numbers, with a relative error of the order of 2^(-2p). Assuming an FMA instruction is available, we perform a tight error analysis of an augmented precision algorithm for the square root, and introduce two slightly different augmented precision algorithms for the 2D-norm sqrt(x^2+y^2). Then we give tight lower bounds on the minimum distance (in ulps) between sqrt(x^2+y^2) and a midpoint when sqrt(x^2+y^2) is not itself a midpoint. This allows us to determine cases when our algorithms make it possible to return correctly-rounded 2D-norms. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1109/ARITH.2011.13 | IEEE Symposium on Computer Arithmetic |
Keywords | Field | DocType |
minimum distance,augmented precision square roots,precision-p floating-point arithmetic,augmented precision algorithm,augmented precision,lower bound,floating-point number,fma instruction,tight error analysis,2-d norms,correctly rounding sqrt,relative error,different augmented precision algorithm,approximation algorithms,linear algebra,polynomials,taylor series,floating point arithmetic,algorithm design and analysis,square root | Approximation algorithm,Discrete mathematics,Algorithm design,Midpoint,Polynomial,Floating point,Rounding,Square root,Approximation error,Mathematics | Conference |
ISSN | Citations | PageRank |
1063-6889 | 0 | 0.34 |
References | Authors | |
13 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nicolas Brisebarre | 1 | 106 | 13.20 |
| Mioara Joldeş | 2 | 110 | 11.53 |
| Peter Kornerup | 3 | 272 | 40.50 |
| Érik Martin-Dorel | 4 | 16 | 3.24 |
| Jean-Michel Muller | 5 | 466 | 66.61 |